Except possibly for high speed downhill situations, wouldn't the horse outperform the bike in most riding situations?
Sometimes if I'm climbing a big, steep hill, I'd gladly trade in my granny gear for a willing horse
A bicycle will obviously make human travel far more efficient. So would a horse. Now...here's the clincher...how about making a bicycle for a horse. Then ride the horse on the bicycle. Lance wouldn't have a chance against you!
1 road bike (simple, light), 1 TT bike (could be more aero, could be lighter), 1 all-weather commuter and winter bike, 1 Monark 828E ergometer indoor bike
Humans actually have greater endurance than horses, typically.
Given a long enough race between a horse and a human, the human should win.
It might require fast walking speeds and several hundred miles, but still.